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In this paper, we analyze classical and quantum physical systems from anoptimal control perspective. Specifically, we explore whether their associateddynamics can correspond to an open or closed-loop feedback evolution of acontrol problem. Firstly, for the classical regime, when it is viewed in termsof the theory of canonical transformations, we find that it can be described bya closed-loop feedback problem. Secondly, for a quantum physical system, if onerealizes that the Heisenberg commutation relations themselves can be thought ofas constraints in a non-commutative space, then the momentum must be dependenton the position for any generic wave function. This implies the existence of aclosed-loop strategy for the quantum case. Thus, closed-loop feedback is anatural phenomenon in the physical world. For the sake of exposition, we give ashort review of control theory, and some familiar examples at the classical andquantum levels are analyzed.

An Optimal Control Perspective on Classical and Quantum Physical Systems